While machine learning (ML) methods have received a lot of attention in recent years, these methods are primarily for prediction. Empirical researchers conducting policy evaluations are, on the other hand, preoccupied with causal problems, trying to answer counterfactual questions: what would have happened in the absence of a policy? Because these counterfactuals can never be directly observed (described as the “fundamental problem of causal inference”) prediction tools from the ML literature cannot be readily used for causal inference. In the last decade, major innovations have taken place incorporating supervised ML tools into estimators for causal parameters such as the average treatment effect (ATE). This holds the promise of attenuating model misspecification issues, and increasing of transparency in model selection. One particularly mature strand of the literature include approaches that incorporate supervised ML approaches in the estimation of the ATE of a binary treatment, under the unconfoundedness and positivity assumptions (also known as exchangeability and overlap assumptions).
This article begins by reviewing popular supervised machine learning algorithms, including trees-based methods and the lasso, as well as ensembles, with a focus on the Super Learner. Then, some specific uses of machine learning for treatment effect estimation are introduced and illustrated, namely (1) to create balance among treated and control groups, (2) to estimate so-called nuisance models (e.g., the propensity score, or conditional expectations of the outcome) in semi-parametric estimators that target causal parameters (e.g., targeted maximum likelihood estimation or the double ML estimator), and (3) the use of machine learning for variable selection in situations with a high number of covariates.
Since there is no universal best estimator, whether parametric or data-adaptive, it is best practice to incorporate a semi-automated approach than can select the models best supported by the observed data, thus attenuating the reliance on subjective choices.
Article
Machine Learning in Policy Evaluation: New Tools for Causal Inference
Noémi Kreif and Karla DiazOrdaz
Article
Macroeconomic Aspects of Housing
Charles Ka Yui Leung and Cho Yiu Joe Ng
This article summarizes research on the macroeconomic aspects of the housing market. In terms of the macroeconomic stylized facts, this article demonstrates that with respect to business cycle frequency, there was a general decrease in the association between macroeconomic variables (MV), such as the real GDP and inflation rate, and housing market variables (HMV), such as the housing price and the vacancy rate, following the global financial crisis (GFC). However, there are macro-finance variables, such as different interest rate spreads, that exhibited a strong association with the HMV following the GFC. For the medium-term business cycle frequency, some but not all patterns prevail. These “new stylized facts” suggest that a reconsideration and refinement of existing “macro-housing” theories would be appropriate. This article also provides a review of the corresponding academic literature, which may enhance our understanding of the evolving macro-housing–finance linkage.
Article
Markov Switching
Yong Song and Tomasz Woźniak
Markov switching models are a family of models that introduces time variation in the parameters in the form of their state, or regime-specific values. This time variation is governed by a latent discrete-valued stochastic process with limited memory. More specifically, the current value of the state indicator is determined by the value of the state indicator from the previous period only implying the Markov property. A transition matrix characterizes the properties of the Markov process by determining with what probability each of the states can be visited next period conditionally on the state in the current period. This setup decides on the two main advantages of the Markov switching models: the estimation of the probability of state occurrences in each of the sample periods by using filtering and smoothing methods and the estimation of the state-specific parameters. These two features open the possibility for interpretations of the parameters associated with specific regimes combined with the corresponding regime probabilities.
The most commonly applied models from this family are those that presume a finite number of regimes and the exogeneity of the Markov process, which is defined as its independence from the model’s unpredictable innovations. In many such applications, the desired properties of the Markov switching model have been obtained either by imposing appropriate restrictions on transition probabilities or by introducing the time dependence of these probabilities determined by explanatory variables or functions of the state indicator. One of the extensions of this basic specification includes infinite hidden Markov models that provide great flexibility and excellent forecasting performance by allowing the number of states to go to infinity. Another extension, the endogenous Markov switching model, explicitly relates the state indicator to the model’s innovations, making it more interpretable and offering promising avenues for development.
Article
Measurement Error: A Primer for Macroeconomists
Simon van Norden
Most applied researchers in macroeconomics who work with official macroeconomic statistics (such as those found in the National Accounts, the Balance of Payments, national government budgets, labor force statistics, etc.) treat data as immutable rather than subject to measurement error and revision. Some of this error may be caused by disagreement or confusion about what should be measured. Some may be due to the practical challenges of producing timely, accurate, and precise estimates. The economic importance of measurement error may be accentuated by simple arithmetic transformations of the data, or by more complex but still common transformations to remove seasonal or other fluctuations. As a result, measurement error is seemingly omnipresent in macroeconomics.
Even the most widely used measures such as Gross Domestic Products (GDP) are acknowledged to be poor measures of aggregate welfare as they omit leisure and non-market production activity and fail to consider intertemporal issues related to the sustainability of economic activity. But even modest attempts to improve GDP estimates can generate considerable controversy in practice. Common statistical approaches to allow for measurement errors, including most factor models, rely on assumptions that are at odds with common economic assumptions which imply that measurement errors in published aggregate series should behave much like forecast errors. Fortunately, recent research has shown how multiple data releases may be combined in a flexible way to give improved estimates of the underlying quantities.
Increasingly, the challenge for macroeconomists is to recognize the impact that measurement error may have on their analysis and to condition their policy advice on a realistic assessment of the quality of their available information.
Article
Mergers and Acquisitions: Long-Run Performance and Success Factors
Luc Renneboog and Cara Vansteenkiste
Despite the aggregate value of M&A market transactions amounting to several trillions dollars on an annual basis, acquiring firms often underperform relative to non-acquiring firms, especially in public takeovers. Although hundreds of academic studies have investigated the deal- and firm-level factors associated with M&A announcement returns, many factors that increase M&A performance in the short run fail to relate to sustained long-run returns. In order to understand value creation in M&As, it is key to identify the firm and deal characteristics that can reliably predict long-run performance.
Broadly speaking, long-run underperformance in M&A deals results from poor acquirer governance (reflected by CEO overconfidence and a lack of (institutional) shareholder monitoring) as well as from poor merger execution and integration (as captured by the degree of acquirer-target relatedness in the post-merger integration process). Although many more dimensions affect immediate deal transaction success, their effect on long-run performance is non-existent, or mixed at best.
Article
Methodology of Macroeconometrics
Aris Spanos
The current discontent with the dominant macroeconomic theory paradigm, known as Dynamic Stochastic General Equilibrium (DSGE) models, calls for an appraisal of the methods and strategies employed in studying and modeling macroeconomic phenomena using aggregate time series data. The appraisal pertains to the effectiveness of these methods and strategies in accomplishing the primary objective of empirical modeling: to learn from data about phenomena of interest. The co-occurring developments in macroeconomics and econometrics since the 1930s provides the backdrop for the appraisal with the Keynes vs. Tinbergen controversy at center stage. The overall appraisal is that the DSGE paradigm gives rise to estimated structural models that are both statistically and substantively misspecified, yielding untrustworthy evidence that contribute very little, if anything, to real learning from data about macroeconomic phenomena. A primary contributor to the untrustworthiness of evidence is the traditional econometric perspective of viewing empirical modeling as curve-fitting (structural models), guided by impromptu error term assumptions, and evaluated on goodness-of-fit grounds. Regrettably, excellent fit is neither necessary nor sufficient for the reliability of inference and the trustworthiness of the ensuing evidence. Recommendations on how to improve the trustworthiness of empirical evidence revolve around a broader model-based (non-curve-fitting) modeling framework, that attributes cardinal roles to both theory and data without undermining the credibleness of either source of information. Two crucial distinctions hold the key to securing the trusworthiness of evidence. The first distinguishes between modeling (specification, misspeification testing, respecification, and inference), and the second between a substantive (structural) and a statistical model (the probabilistic assumptions imposed on the particular data). This enables one to establish statistical adequacy (the validity of these assumptions) before relating it to the structural model and posing questions of interest to the data. The greatest enemy of learning from data about macroeconomic phenomena is not the absence of an alternative and more coherent empirical modeling framework, but the illusion that foisting highly formal structural models on the data can give rise to such learning just because their construction and curve-fitting rely on seemingly sophisticated tools. Regrettably, applying sophisticated tools to a statistically and substantively misspecified DSGE model does nothing to restore the trustworthiness of the evidence stemming from it.
Article
Mixed Frequency Models
Eric Ghysels
The majority of econometric models ignore the fact that many economic time series are sampled at different frequencies. A burgeoning literature pertains to econometric methods explicitly designed to handle data sampled at different frequencies. Broadly speaking these methods fall into two categories: (a) parameter driven, typically involving a state space representation, and (b) data driven, usually based on a mixed-data sampling (MIDAS)-type regression setting or related methods. The realm of applications of the class of mixed frequency models includes nowcasting—which is defined as the prediction of the present—as well as forecasting—typically the very near future—taking advantage of mixed frequency data structures. For multiple horizon forecasting, the topic of MIDAS regressions also relates to research regarding direct versus iterated forecasting.
Article
Modeling Chronic Diseases in Relation to Risk Factors
Pieter van Baal and Hendriek Boshuizen
In most countries, non-communicable diseases have taken over infectious diseases as the most important causes of death. Many non-communicable diseases that were previously lethal diseases have become chronic, and this has changed the healthcare landscape in terms of treatment and prevention options. Currently, a large part of healthcare spending is targeted at curing and caring for the elderly, who have multiple chronic diseases. In this context prevention plays an important role, as there are many risk factors amenable to prevention policies that are related to multiple chronic diseases.
This article discusses the use of simulation modeling to better understand the relations between chronic diseases and their risk factors with the aim to inform health policy. Simulation modeling sheds light on important policy questions related to population aging and priority setting. The focus is on the modeling of multiple chronic diseases in the general population and how to consistently model the relations between chronic diseases and their risk factors by combining various data sources. Methodological issues in chronic disease modeling and how these relate to the availability of data are discussed. Here, a distinction is made between (a) issues related to the construction of the epidemiological simulation model and (b) issues related to linking outcomes of the epidemiological simulation model to economic relevant outcomes such as quality of life, healthcare spending and labor market participation. Based on this distinction, several simulation models are discussed that link risk factors to multiple chronic diseases in order to explore how these issues are handled in practice. Recommendations for future research are provided.
Article
Noncompliance and Missing Data in Health Economic Evaluation
Karla DiazOrdaz and Richard Grieve
Health economic evaluations face the issues of noncompliance and missing data. Here, noncompliance is defined as non-adherence to a specific treatment, and occurs within randomized controlled trials (RCTs) when participants depart from their random assignment. Missing data arises if, for example, there is loss-to-follow-up, survey non-response, or the information available from routine data sources is incomplete. Appropriate statistical methods for handling noncompliance and missing data have been developed, but they have rarely been applied in health economics studies. Here, we illustrate the issues and outline some of the appropriate methods with which to handle these with application to health economic evaluation that uses data from an RCT.
In an RCT the random assignment can be used as an instrument-for-treatment receipt, to obtain consistent estimates of the complier average causal effect, provided the underlying assumptions are met. Instrumental variable methods can accommodate essential features of the health economic context such as the correlation between individuals’ costs and outcomes in cost-effectiveness studies. Methodological guidance for handling missing data encourages approaches such as multiple imputation or inverse probability weighting, which assume the data are Missing At Random, but also sensitivity analyses that recognize the data may be missing according to the true, unobserved values, that is, Missing Not at Random.
Future studies should subject the assumptions behind methods for handling noncompliance and missing data to thorough sensitivity analyses. Modern machine-learning methods can help reduce reliance on correct model specification. Further research is required to develop flexible methods for handling more complex forms of noncompliance and missing data.
Article
Nonlinear Models in Macroeconometrics
Timo Teräsvirta
Many nonlinear time series models have been around for a long time and have originated outside of time series econometrics. The stochastic models popular univariate, dynamic single-equation, and vector autoregressive are presented and their properties considered. Deterministic nonlinear models are not reviewed. The use of nonlinear vector autoregressive models in macroeconometrics seems to be increasing, and because this may be viewed as a rather recent development, they receive somewhat more attention than their univariate counterparts. Vector threshold autoregressive, smooth transition autoregressive, Markov-switching, and random coefficient autoregressive models are covered along with nonlinear generalizations of vector autoregressive models with cointegrated variables. Two nonlinear panel models, although they cannot be argued to be typically macroeconometric models, have, however, been frequently applied to macroeconomic data as well. The use of all these models in macroeconomics is highlighted with applications in which model selection, an often difficult issue in nonlinear models, has received due attention. Given the large amount of nonlinear time series models, no unique best method of choosing between them seems to be available.
Article
Outlier Detection
Bent Nielsen
This is an advance summary of a forthcoming article in the Oxford Research Encyclopedia of Economics and Finance. Please check back later for the full article.
Detection of outliers is an important explorative step in empirical analysis. Once detected, the investigator will have to decide how to model the outliers depending on the context. Indeed, the outliers may represent noisy observations that are best left out of the analysis or they may be very informative observations that would have a particularly important role in the analysis. For regression analysis in time series a number of outlier algorithms are available, including impulse indicator saturation and methods from robust statistics. The algorithms are complex and their statistical properties are not fully understood. Extensive simulation studies have been made, but the formal theory is lacking. Some progress has been made toward an asymptotic theory of the algorithms. A number of asymptotic results are already available building on empirical process theory.
Article
Persistence Change and Segmented Cointegration Testing
Paulo M. M. Rodrigues
The change in persistence of a time series refers to a shift in the order of integration. Rather than displaying stationary or nonstationary behavior throughout the whole sample period, as is frequently considered in empirical work, many time series display changes in persistence over time. The analysis and impact of possible changes in persistence has been an important topic of research and has led to a large literature devoted to the development of procedures to detect such behavior. This review explores different tests designed to detect changes in the persistence and in the long-run equilibrium of time series.
Article
Predictive Regressions
Jesús Gonzalo and Jean-Yves Pitarakis
Predictive regressions are a widely used econometric environment for assessing the predictability of economic and financial variables using past values of one or more predictors. The nature of the applications considered by practitioners often involve the use of predictors that have highly persistent, smoothly varying dynamics as opposed to the much noisier nature of the variable being predicted. This imbalance tends to affect the accuracy of the estimates of the model parameters and the validity of inferences about them when one uses standard methods that do not explicitly recognize this and related complications. A growing literature aimed at introducing novel techniques specifically designed to produce accurate inferences in such environments ensued. The frequent use of these predictive regressions in applied work has also led practitioners to question the validity of viewing predictability within a linear setting that ignores the possibility that predictability may occasionally be switched off. This in turn has generated a new stream of research aiming at introducing regime-specific behavior within predictive regressions in order to explicitly capture phenomena such as episodic predictability.
Article
Preferential Trade Agreements: Recent Theoretical and Empirical Developments
James Lake and Pravin Krishna
In recent decades, there has been a dramatic proliferation of preferential trade agreements (PTAs) between countries that, while legal, contradict the non-discrimination principle of the world trade system. This raises various issues, both theoretical and empirical, regarding the evolution of trade policy within the world trade system and the welfare implications for PTA members and non-members. The survey starts with the Kemp-Wan-Ohyama and Panagariya-Krishna analyses in the literature that theoretically show PTAs can always be constructed so that they (weakly) increase the welfare of members and non-members. Considerable attention is then devoted to recent developments on the interaction between PTAs and multilateral trade liberalization, focusing on two key incentives: an “exclusion incentive” of PTA members and a “free riding incentive” of PTA non-members. While the baseline presumption one should have in mind is that these incentives lead PTAs to inhibit the ultimate degree of global trade liberalization, this presumption can be overturned when dynamic considerations are taken into account or when countries can negotiate the degree of multilateral liberalization rather than facing a binary choice over global free trade. Promising areas for pushing this theoretical literature forward include the growing use of quantitative trade models, incorporating rules of origin and global value chains, modeling the issues surrounding “mega-regional” agreements, and modelling the possibility of exit from PTAs. Empirical evidence in the literature is mixed regarding whether PTAs lead to trade diversion or trade creation, whether PTAs have significant adverse effects on non-member terms-of-trade, whether PTAs lead members to lower external tariffs on non-members, and the role of PTAs in facilitating deep integration among members.
Article
Publication Bias in Asset Pricing Research
Andrew Y. Chen and Tom Zimmermann
Researchers are more likely to share notable findings. As a result, published findings tend to overstate the magnitude of real-world phenomena. This bias is a natural concern for asset pricing research, which has found hundreds of return predictors and little consensus on their origins.
Empirical evidence on publication bias comes from large-scale metastudies. Metastudies of cross-sectional return predictability have settled on four stylized facts that demonstrate publication bias is not a dominant factor: (a) almost all findings can be replicated, (b) predictability persists out-of-sample, (c) empirical t-statistics are much larger than 2.0, and (d) predictors are weakly correlated. Each of these facts has been demonstrated in at least three metastudies.
Empirical Bayes statistics turn these facts into publication bias corrections. Estimates from three metastudies find that the average correction (shrinkage) accounts for only 10%–15% of in-sample mean returns and that the risk of inference going in the wrong direction (the false discovery rate) is less than 10%.
Metastudies also find that t-statistic hurdles exceed 3.0 in multiple testing algorithms and that returns are 30%–50% weaker in alternative portfolio tests. These facts are easily misinterpreted as evidence of publication bias. Other misinterpretations include the conflating of phrases such as “mostly false findings” with “many insignificant findings,” “data snooping” with “liquidity effects,” and “failed replications” with “insignificant ad-hoc trading strategies.”
Cross-sectional predictability may not be representative of other fields. Metastudies of real-time equity premium prediction imply a much larger effect of publication bias, although the evidence is not nearly as abundant as it is in the cross section. Measuring publication bias in areas other than cross-sectional predictability remains an important area for future research.
Article
Quality in Nursing Homes
Matteo Lippi Bruni, Irene Mammi, and Rossella Verzulli
In developed countries, the role of public authorities as financing bodies and regulators of the long-term care sector is pervasive and calls for well-planned and informed policy actions. Poor quality in nursing homes has been a recurrent concern at least since the 1980s and has triggered a heated policy and scholarly debate. The economic literature on nursing home quality has thoroughly investigated the impact of regulatory interventions and of market characteristics on an array of input-, process-, and outcome-based quality measures. Most existing studies refer to the U.S. context, even though important insights can be drawn also from the smaller set of works that covers European countries.
The major contribution of health economics to the empirical analysis of the nursing home industry is represented by the introduction of important methodological advances applying rigorous policy evaluation techniques with the purpose of properly identifying the causal effects of interest. In addition, the increased availability of rich datasets covering either process or outcome measures has allowed to investigate changes in nursing home quality properly accounting for its multidimensional features.
The use of up-to-date econometric methods that, in most cases, exploit policy shocks and longitudinal data has given researchers the possibility to achieve a causal identification and an accurate quantification of the impact of a wide range of policy initiatives, including the introduction of nurse staffing thresholds, price regulation, and public reporting of quality indicators. This has helped to counteract part of the contradictory evidence highlighted by the strand of works based on more descriptive evidence. Possible lines for future research can be identified in further exploration of the consequences of policy interventions in terms of equity and accessibility to nursing home care.
Article
Quantile Regression for Panel Data and Factor Models
Carlos Lamarche
For nearly 25 years, advances in panel data and quantile regression were developed almost completely in parallel, with no intersection until the work by Koenker in the mid-2000s. The early theoretical work in statistics and economics raised more questions than answers, but it encouraged the development of several promising new approaches and research that offered a better understanding of the challenges and possibilities at the intersection of the literatures. Panel data quantile regression allows the estimation of effects that are heterogeneous throughout the conditional distribution of the response variable while controlling for individual and time-specific confounders. This type of heterogeneous effect is not well summarized by the average effect. For instance, the relationship between the number of students in a class and average educational achievement has been extensively investigated, but research also shows that class size affects low-achieving and high-achieving students differently. Advances in panel data include several methods and algorithms that have created opportunities for more informative and robust empirical analysis in models with subject heterogeneity and factor structure.
Article
Quasi Maximum Likelihood Estimation of High-Dimensional Factor Models
Matteo Barigozzi
Factor models are some of the most common dimension reduction techniques in time series econometrics. They are based on the idea that each element of a set of N time series is made of a common component driven by few latent factors capturing the main comovements among the series, plus idiosyncratic components often representing just measurement error or at most being weakly cross-sectionally correlated with the other idiosyncratic components. When N is large the factors can be retrieved by cross-sectional aggregation of the observed time series. This is the so-called blessing of dimensionality, meaning that having N growing to infinity poses no estimation problem but in fact is a necessary condition for consistent estimation of the factors and for identification of the common and idiosyncratic components.
There exist two main ways to estimate a factor model: principal component analysis and maximum likelihood estimation. The former method is more recent and more common in econometrics, but the latter, which is the classical approach, has many appealing features such as allowing one to impose constraints, deal with missing values, and explicitly model the dynamic of the factors. Maximum likelihood estimation of large factor models has been studied in two influential papers: Doz et al.’s “A Quasi Maximum Likelihood Approach for Large Approximate Dynamic Factor Models” and Bai and Li’s “Maximum Likelihood Estimation and Inference for Approximate Factor Models of High Dimension.” The latter considers the static case, which is closer to the classical approach and no model for the factors is assumed, and the former is more general: it considers estimation combined with the use of Kalman filtering techniques, which has grown popular in macroeconomic policy analysis.
Those two papers, together with other recent results, have brought new asymptotic results for which a synthesis is provided. Special attention is paid to the set of assumptions, which is taken to be the minimal set of assumptions required to get the results.
Article
Real-Time Transaction Data for Nowcasting and Short-Term Economic Forecasting
John W. Galbraith
Transaction data from consumer purchases is used for monitoring, nowcasting, or short-term forecasting of important macroeconomic aggregates such as personal consumption expenditure and national income. Data on individual purchase transactions, recorded electronically at point of sale or online, offer the potential for accurate and rapid estimation of retail sales expenditure, itself an important component of personal consumption expenditure and therefore of national income. Such data may therefore allow policymakers to base actions on more up-to-date estimates of the state of the economy. However, while transaction data may be obtained from a number of sources, such as national payments systems, individual banks, or financial technology companies, data from each of these sources contain limitations.
Data sets will differ in the forms of information contained in a record, the degree to which the samples are representative of the relevant population of consumers, and the different types of payments that are observed and captured in the record. As well, the commercial nature of the data may imply constraints on the researcher’s ability to make data sets available for replication. Regardless of the source, the data will generally require filtering and aggregation in order to provide a clear signal of changes in economic activity.
The resulting series may be incorporated into any of a variety of model types, along with other data, for nowcasting and short-term forecasting.
Article
Reduced Rank Regression Models in Economics and Finance
Gianluca Cubadda and Alain Hecq
Reduced rank regression (RRR) has been extensively employed for modelling economic and financial time series. The main goals of RRR are to specify and estimate models that are capable of reproducing the presence of common dynamics among variables such as the serial correlation common feature and the multivariate autoregressive index models. Although cointegration analysis is likely the most prominent example of the use of RRR in econometrics, a large body of research is aimed at detecting and modelling co-movements in time series that are stationary or that have been stationarized after proper transformations. The motivations for the use of RRR in time series econometrics include dimension reductions, which simplify complex dynamics and thus make interpretations easier, as well as the pursuit of efficiency gains in both estimation and prediction. Via the final equation representation, RRR also makes the nexus between multivariate time series and parsimonious marginal ARIMA (autoregressive integrated moving average) models. RRR’s drawback, which is common to all of the dimension reduction techniques, is that the underlying restrictions may or may not be present in the data.
